IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

1A Model to Explain the Emergence of Imitation
Development based on Predictability Preference
Takashi Minato, Dale Thomas, Yuichiro Yoshikawa, and Hiroshi Ishiguro, Member, IEEE

Abstract—Imitation is a very complicated function which
requires a body mapping (a mapping from observed body motions
to motor commands) that can discriminate between self motions
and those of others. The developmental mechanism of thissophisticated capability, and the order in which the required
abilities arise, is poorly understood. In this article, we present amechanism for the development of imitation through a simulationof infant-caregiver interaction. A model was created to acquire abody mapping, which is necessary for successful mutual imitation
in infant-caregiver interaction, while discriminating self-motion
from the motion of the other. The ability to predict motions andthe time delay between performing a motion and observing any
correlated motion provides clues to assist the development of the
body mapping. The simulation results show that the developmentof imitation capabilities depends on a predictability preference (afunction of how an agent feels regarding its options of ‘what toimitate,’ given its ability to predict motions). In addition, the simulated infants in our system are able to develop the components
of a healthy body mapping in order, that is, relating self motion
first, followed by an understanding of others’ motions. This orderof development emerges spontaneously without the need for any
explicit mechanism or any partitioning of the interaction. These
results suggest that this predictability preference is an importantfactor in infant development.
Index Terms—infant development, imitation, body mapping,self-other distinction, predictability preference,

I. I NTRODUCTION
Imitation is a very important function in human infantdevelopment, especially for the development of our ability
to understand and communicate with others. For example,
simulation theory has suggested that the capacity to understandothers’ internal state relies on a process which matches theobserved behavior with the action of the observer, that is,imitation by the observer [1]. According to Piaget’s developmental theory [2], infants’ imitative behaviors (shown in
TABLE I) are observed while the infants learn to coordinate
their senses and motor skills in the first two years. Before
infants come to be able to imitate other persons in stage
3, they show repetitive behaviors (it seems they are mainly
attentive to their own bodies) in stage 2. This process (fromstage 2 to 3) has also been observed in other studies [3]. It
is suggested that infants develop a sense of ’self’ after birth[4], that is, the self-knowledge of infants is formed during
the developmental process. It may be that infants are unable
to distinguish self-produced motions from motions producedby others within their perception in the early developmental
Asada Project, ERATO, Japan Science and Technology Agency, Graduate
School of Engineering, Osaka University, Suita, Osaka, 565-0871, Japan, email:minato@atr.jp.
Manuscript received Month Date, Year; revised Month Date, Year.

TABLE II NFANT BEHAVIORS IN P IAGET ’ S STAGES OF COGNITIVE DEVELOPMENT.
Stage (Age)Stage 1
(0–1 month)Stage 2
(1–4 months)

Stage 3
(4–8 months)

Stage 4
(8–12 months)

Stage 5
(12–18 months)
Stage 6(18–24 months)

Infants’ behaviors
Infants operate based on reflexes.
Infants show primary circular reactions (reproductionof an interesting event initially occurred by chance)
involving their own bodies (e.g., repeating the motionof passing their hand before their face).
Infants actively experience the effects their behaviors
on external objects and repeat actions to bring about adesirable consequence (secondary circular reactions).
Infant imitates an adult who is imitating him/her.
Infants coordinate actions into new and more complex
sequences and start to show intentional, goal-directedbehaviors. Infants can imitate behaviors without feedback (e.g., facial gestures).
Infants experiment with new behavior in a purposeful,trial-and-error way (tertiary circular reactions). Infants
actively imitate new behaviors.
Infants develop the ability to use primitive symbols.
Infants become capable of deferred imitation and start
to solve certain types of problems mentally.

process. However, infants come to repeat their own motions inadvance of imitating others even though they are frequently inthe presence of other people (caregivers) and they may observe
not only self-produced motions but also movements producedby others. In primary circular reactions, infants may be unable
to recognize ’their body’ motions but just respond to interesting events, however, it is considered that these reactions work
as self-imitation for the development of infant’s sensorimotor
coordination [5]. We infer that the infant acquires the ability to
distinguish self from others during this process (the transition
from self to mutual imitation). This developmental process is
considered to be essential for imitation development. However,not many studies have focused on this mechanism. This paper
focuses on the mechanism of the transition from self to mutual
imitation in the process of acquiring a body mapping.
Imitation requires a body mapping that associates anobserved motion with the corresponding motor commands
needed to perform the same action. Although some studies
have suggested that infants have an innate body mapping, andthere have been some examples of neonates imitating theirparents in some manner (ex., [6]), we consider a neonate’s
body mapping to be not sufficiently innate and that it isacquired, at least in part, through sensorimotor experiences
after birth (ex., [7]). Self-imitation requires a mapping thatassociates an observed self-motion with the corresponding
motor command (hereafter called the ‘self-model’), whileother-imitation needs a mapping that associates an observed
other-motion with the corresponding motor command (here-

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

after called the ‘other-model’). The development of imitation
capabilities should involve the acquisition of these two models,with which self and other’s motions become distinguishable.
This paper accounts for it as the development of self-otherdistinction in the body mapping acquisition.
Some studies have focused on the mechanisms of bodymapping acquisition. Oztop and Arbib [8] proposed a model toacquire a body mapping related to grasping motions througha hand state which is a viewpoint-independent image feature.
An alternative clue, which aids the learning of the bodymapping, is when the learner is imitated by another person.
In fact, it has been reported that caregivers frequently imitate
their baby in various situations, especially in vocal interaction(ex., [9–13]). Ishihara et al. [14] proposed a model in whichinfants learn how to vocalize vowels through mutual imitation
with caregivers. Yokoya et al. [15] suggested that a bodymapping is acquired through the process of being imitatedby another person. However, these studies assumed that otherpersons (caregivers) can already be discriminated from self
and that the self-model is acquired first and then followedby the acquisition of the other-model based on the priorlearned self-model. This explicit partitioning of interaction
does not happen in real world situations; that is, at no point
do infants get an opportunity to fully develop their self-modelin the absence of any other environmental factors and only
then start to have caregivers interact with them. Rather, theinfants themselves must possess an innate mechanism that
automatically causes the developmental order, beginning withthe self-model acquisition and proceeding to the acquisitionof the other-model, to emerge spontaneously.
This paper reports a study of a mechanism behind thedevelopment of an infant’s body mapping which enables selfimitation and the ability to imitate others through infantcaregiver interaction. This mechanism concerns the acquisitionof imitation capabilities and the ability to distinguish selffrom others in the circumstance of being with a caregiver. We
study the mechanism through a computer simulation of infantcaregiver interaction in the standpoint of the constructivist
approach called Cognitive Developmental Robotics [16]. Since
the study on the mechanism of imitation development is
an intricate issue, imitation development was simplified into
the acquisition of self-model and other-model through infantcaregiver interaction and, in addition, essential factors forbringing about the transition from self to mutual imitation
were explored. We built a minimal model to represent the
body mapping and simulated interactions between infant andcaregiver. We focused only on the imitative behaviors of theinfant and the caregiver in their interaction and did not specify
their task explicitly. In order to learn the body mapping, theinfant needs to be imitated by the caregiver, and also theinfant needs to imitate the caregiver because it is consideredthat the caregiver’s imitative behavior is elicited when he/she
is imitated [17]. At first the infant cannot correctly imitate
because of his/her immature body mapping and proceeds tolearn the mapping through the imitative interaction. During
this interaction, the agents need to choose a motion fromone corresponding to self motion (self-imitation) and one
corresponding to the other’s motion (imitating other). This

2

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motion selection problem possibly relies on the predictabilityof the observation since it has been observed that infants
are highly sensitive to contingency [18, 19]. We propose amechanism for the motion decision that uses a predictability
preference, which is the preference for a motion modulatedby the predictability. It is expected that the infant does notacquire the body mapping if the caregiver never imitates theinfant, because we assume the body mapping is constructedowing to the other’s imitation. It is also expected that the
infant is unable to discriminate self from other if the infant
and caregiver keep imitating each other with the same motion
because the self motor command can be matched equally withboth the observed self-motion and the other’s motion. It isinferred that the motion selection affects the course of theinteraction and the development of imitation. This paper showsthat the predictability preference which is typical for healthypeople can lead to the successful learning of body mapping. It
is generally desired that a developmental model can reproduce
not only typical development but also disordered development
when the model has some deficits in order to improve the validity of the model. We also investigate imitation development
when the infant has an atypical predictability preference. It issuggested that the predictability preference is one of the mostimportant factors governing the development of body mapping,which involves the development of self-other distinction andimitation, by showing how a typical preference results in a
typical developmental process and atypical preferences leadto a disordered body mapping.
II. A MODEL FOR THE EMERGENCE OF IMITATIONDEVELOPMENT

This paper studies a mechanism behind the development ofself-imitation and the imitation of others. The main focus is to
explore the infant’s mechanism that automatically causes thedevelopmental order to emerge spontaneously. Our model does
not include the explicit mechanism of developmental sequenceor specific tasks. This differentiates our model from those of
the existing studies.
In order to deal with this issue in the computer simulation,
we built a minimal model to represent the body mapping andthe infant-caregiver interaction. To simplify the model, we
make the following assumptions:• Body motions are spatially and temporally discretized.
The motion segmentation problem, that is, knowing whena discrete motion begins and ends, is also important ininfant development. The capabilities of the segmentationand the self-other distinction might develop in parallel
and influence each other. However, we assume that the

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX$JHQW¶VYLHZ

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The caregiver has a perfect body mapping, while theinfant does not know the correct correspondence andcannot initially distinguish between observed self andother motions.
The infant imitates by executing a body motion whichcorresponds to the observed body motion according tohis/her immature body mapping.
• The infant learns the body mapping using unsupervised
learning, that is, without any explicit reward.
The infant cannot know whether or not his/her imitation
is successful because of his/her immature body mapping.
It is observed, in fact, that the caregiver indicates that theimitation is successful by giving a reward. However, thereward is not always expected in the infant-caregiver interaction. This paper deals with the extreme case in which
no reward is given by the caregiver. The body mappingis learned simply by associating motor commands withobserved motions.
• The agent can predict the successive observation fromthe self motor command by using the body mapping
inversely.
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motion segmentation capability is acquired in advance.
This is indeed a large assumption, but was made for thesake of keeping the model tractable.
• Both the infant and the caregiver have homologous body
motions.
• The agents show motion either by trying to imitate, orby selecting an action to be performed randomly (here,“agent” denotes infant or caregiver). Also, no explicit task
is given to either agent.
The agent’s motion is categorized into imitation or othermotions in order to focus only on imitation which isnecessary for the body mapping acquisition.
• Both agents perform a body motion at the same time andobserve both their own motion and that of the other. An
example of infant-caregiver interaction is shown in Fig.1.
The caregiver in time step t+2 shows an imitative motion(the caregiver observes the infant’s right hand movementin time step t + 1 and shows the same motion in time
step t + 2). To the contrary, the caregiver in time stept + 1 does not show an imitative motion, i.e., performs
a randomly selected motion (the infant’s motion in time
step t is left hand movement but the caregiver’s motion intime step t + 1 is right hand movement). A body motion
is assumed to be a motion pattern of arms and legs which
can be seen by the agent himself such as a waving handin front of the face.
The self-other distinction can be explained as an issue todiscriminate between observed motions with perfect contingency (observed self-motions), with imperfect contingency (observed other’s imitative motions), and with nocorrelation to the self-motion. We have this assumption
to present situations including these observations.

The body mapping is represented by a network as shownin Fig.2. The body motions in the observation and the motor
command are discretized. An observed body motion is represented by one node in the visual representation layer andthe motor commands for a body motion are represented by asingle node in the motor representation layer. For the sake of
convenience, the observed self-motions are displayed in theleft half of the visual representation layer and the observed
other’s motions are displayed in the right half, though thelearning rules do not discriminate between the sources of the
body motions. The meanings of the commands in the motor
representation layer are duplicated (i.e., two nodes indicate thesame motion command) by which the infant can acquire two
mappings: a mapping that associates an observed self-motion
with the corresponding self-motor command (self-model) anda mapping that associates an observed other’s motion with thecorresponding self-motor command (other-model). When theagent imitates the observed motion, it is done by executing
a body motion which corresponds to the observed motion
according to the agent’s body mapping.
Initially, the infant’s connections between the visual representation layer and the motor representation layer are immature (i.e. connected with small random weights), as shown in
Fig.3, and develop over the course of the imitation period
according to the interaction with the caregiver. A Hebbian

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

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learning rule reinforces associations between the self-motor
commands with the corresponding body motion observed at
the same time that the motor command is executed. The
caregiver has a perfect body mapping in which the selfmodel and other-model are correctly separated and both layers
are correctly connected (Fig.3). The infant acquires the bodymapping if he/she associates the correct motor commands withthe observed caregiver’s imitative motions.
In order to discriminate between observed self generated
motions and those of the other, the self-model and the othermodel need to be represented separately. One of the clues
needed by the learner in order to acquire these separate
models is a difference in the delay of observation. When amotor command is executed, the corresponding self generated
motion is observed immediately after the execution, while thecorresponding other’s motion is observed with a one step delay(assuming that the other is imitating). In order to make use of
the difference in the delay of observation, the body mapping
model is assumed to have a structure in which the motor
command is copied back to the motor representation layer
in two ways: without delay and with a one step delay. Thisis equivalent to an efferent copy of a motor command. For
the sake of convenience, the motons in the left part of the
motor representation layer shown in Fig.2 (motor commands
copied without delay) is called the self-related motions, andthe motions in the right part (motor commands copied with aone step delay) is called the other-related motions.
The simulation proceeds as follows: (a) The agents executea motor command, (b) The learner updates the body mapping,and (c) The agents select a new motion to perform as shownin Fig.4.
(a) The current motor command and the previous motor
command are copied to the motor representation layer(Ms′ and Mo′ ) when the motor command is executed.
The resulting observations are predicted (Vs′ and Vo′ )from Ms′ and Mo′ with the inverse mapping of the bodymapping.
(b) The body mapping is updated by strengthening the connection weights between the observed motions (V ) andthe copied motor commands on the motor representation
layer (Ms′ and Mo′ ) using a modified Hebbian learning
rule.
(c) The motions corresponding to the observed motions arefound by the body mapping (Ms and Mo ), and theprediction errors (Es and Eo ) are calculated from V ,Vs′ , and Vo′ . The next motion is chosen between Ms andMo based on the prediction errors.
Since the agents observe two motions (self-motion andother’s motion) at the same time, two motions (self-related motion and other-related motion) are retrieved from the observed
motions as shown in Fig.4 (c). When the agents imitate the observed motions they must choose an imitative motion from two
motions. The self-related motion means imitating self-motion(self-imitation) and the other-related motion means imitating
the other’s motion. We hypothesize that the agents choose themotion based on the predictability of the observation. This
paper proposes a predictability preference for motion decision,
which is an innate function relating predictability to action
selection. The agents predict the resulting observations fromthe activations in the motor representation layer by invertingIEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX
1

Preference

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the body mapping (the self-model and other-model are notdiscriminated). Two patterns of the observation (Vs′ and Vo′ )are predicted from the copied current motor command Ms′ andprevious motor command Mo′ as shown in Fig.4 (a). When theagents observe the motions, two prediction errors (Es and Eo )are calculated, which are related to Ms′ and Mo′ , respectively.
The preferences for the self-related and other-related motions(Ps , Po ∈ [0, 1]) are determined based on the prediction errors
Es and Eo , respectively. The preference curve modulates thepreference of a motion based on the prediction error, as shownin Fig.5. The preference is assumed to be determined not onlyby the current prediction error but also the prediction errors
in the past several steps; here the averaged prediction errors(Ēs , Ēo ∈ [0, 1]) are used. In addition, both agents can choosea random motion (Mr ) as an additional option as well as
imitative motions. The preference for the random motion isdefined as Pr = 1 − max(Ps , Po ) so that Pr has a high value
when both the preferences for imitative motions have low
values. The agents probabilistically choose a motion among
Ms , Mo , and Mr in proportion to the ratio of Ps , Po , and Pr .
If the body mapping is correct, the self-motion is correctlypredicted from Ms′ . The other’s motion is correctly predictedfrom Mo′ only when the other imitates. The agent’s action
selection affects the other’s prediction error, and therefore
determines the balance between self-imitation, imitating other,and randomly selected motion, which in turn affects the courseof the interaction and the development of imitation.
The update uses a modified Hebbian learning rule whichtakes mutual exclusivity into consideration [20]. Let wij be
the connection weight between node i in the perception layer
p and node j in the motor representation layer m. The crossanchoring Hebbian learning rule is given by:(1)

This is the update rule for the connection between the mostactivated nodes, where η is the learning rate, i∗ and j ∗ are themost activated nodes in their respective layers, p ai∗ , m aj ∗ ∈[0, 1] are their respective activations and p dij and m dij are thedynamic anchoring rates, given by the following equations:( ∑)k,k̸=j wikpdij = exp −
,
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anchoring. The remaining connections are updated as follows:
wij ∗ (t) = wij ∗ (t − 1) − ηp (1 − p dij ∗ )∆wi∗ j ∗ ,wi∗ j (t) = wi∗ j (t − 1) − ηm (1 − m di∗ j )∆wi∗ j ∗ ,

(4)
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where ηp and ηm are constant coefficients of the competition.
This means that learning is greater when there is more mutual
exclusivity. For situations where such behavior is desired, thatis, if the task calls for mutually exclusive networks, and this is
known a priori, this modified Hebbian learning rule can resultin a significant speedup in learning. This learning procedure
is applied four times per time step, once for each combinationof self/other observations and self/other motor representation
pairs.
III. S IMULATIONS FOR EMERGENCY OF IMITATIONDEVELOPMENT

A. Simulation settings
In order for the learner to acquire the body mapping andimitation capability, he/she needs to elicit imitative motions
from the caregiver. Too much imitation from the caregivermight make it difficult for the learner to discriminate theirown motions from those of the caregiver, whereas too little
imitation will not allow the learner to fully develop a correct
mapping for self and other motions. A good caregiver shouldbe able to strike the right balance of imitation to allow
the infant to develop their body mappings naturally, and thelearner needs to be able to elicit the right balance of imitation.
In our model, the preference curve determines this balance ofimitation. We hypothesize that a typical, healthy preference
leads to a typical developmental process and an atypicalpreference can only result in a disordered body mapping.
We investigated the effects of using different shaped preference curves on the developmental process of the bodymapping. In this simulation, we tested eight distinct preference curves for the learner. The profiles of the curves are
qualitatively different, as shown in Fig.6.
The prediction error of the preference curve (the abscissain Fig.5) essentially indicates a measure of novelty in the
resultant observation. We set the range of preference values
to [0.1, 0.9] so as to avoid extreme cases (e.g., the agent
always preferring the self-related motions). The meanings ofthe preference curves are:
A Nothing: Mostly choose random behavior, regardless of
predictability
B Everything: Mostly try to imitate, regardless of predictability

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

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C Comfort zone: Prefer neither too much familiarity, nor
too much novelty
D Extremes: Prefer very familiar or very novel situations
E Novelty avoiding: Dislike very novel situations
F Familiarity avoiding: Dislike very familiar situations
G Novelty greedy: Prefer very novel situations
H Familiarity greedy: Prefer very familiar situations
Preference curve (C) simulates a Wundt curve where greatest pleasure comes from a moderate amount of stimulus
novelty, which is considered to be a person’s intrinsic preference [21]. It shows a characteristic that the agent does
not prefer motions from which successive results can be
accurately predicted (i.e., results are too-familiar) and cannot
be completely predicted (i.e., results are too-novel). This curveshows a inverted-U relationship between novelty (opposite
of familiarity) and preference. Many studies have argued theinverted-U relationship (ex., [22,23]) and have shown that thiskind of relationship appears in psychological experiments (ex.,[24, 25]). The caregiver was assumed to be a typical healthy
person, and was therefore given this preference curve.
The simulation assumes that the agents have Na patternsof body motion (Na = 30 in this work). The range ofthe connection weights of the body mapping is [0, 1], andthe learner’s initial weights are set randomly in the rangeof [0, 0.1]. The caregiver has a value of 1.0 on the correctconnections and 0.0 on the wrong connections; these are fixedand do not change during the simulation. In the prediction
phase, we assume that the agent predicts motions whose values
are greater than a threshold (0.1) in the visual representation
layer after the inverse mapping is calculated (Vs′ and Vo′ in

Fig.4 (a)). The prediction errors Es and Eo are calculated as
the ratio of the number of predicted but unobserved motions to
the total number of predicted motions. The averaged predicted
errors Ēs and Ēo are calculated from the errors in the last 20
steps. In this work, the learning rate η was set at 0.05, ηp andηm were 0.5, the weights wij were clamped to the range [0, 1]
1
and p σ and m σ were both set to Na4 , which, in this work, was
2.34.
B. Results
The averaged simulation results of 20 trials are shownin Fig.7. One trial is terminated at 10000 time steps. The
caregiver always uses preference curve (C), and each columnof the figure shows the graphs when the infant is using curves(A)-(H). Each row in the figure shows the following results:(1) Acquired mapping of the infant.
The network shows the qualitative features of the mapping acquired by the learner. Solid lines means that over
80% of the correctly corresponding connections havestrong weight (more than 0.5), dashed lines means that
20% to 80% have a strong weight, and with less thanthat no lines are drawn.
(2) Ratio of wrong connections in the infant’s mapping.
The graph shows ratios of the number of motions which
are not correctly connected in the learner’s self-modeland other-model. The abscissa shows the simulation time
step [0, 10000] (the same for each row). Here, we count acorrect connection as follows: when a connection froma node in the visual representation layer has maximal

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

1

1

Mr

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The rates of selected motion for preferences C (same as those inweight among the connections from the node, it iscorrectly connected to the corresponding node in the
motor representation layer, and the difference between
its weight and the second maximal weight is more than athreshold (0.5), we count it as a correct connection. The
threshold is used to check exclusivity of the connection.
(3) Rate of selected motion in the infant’s action selection.
The graph shows rates of the number of times the selfrelated motion Ms , the other-related motion Mo , and therandom motion Mr are selected by the learner in the last
20 steps (the sum of them is always 1.0).
(4) Rate of selected motion in the caregiver’s action selection.
The same as (3) for the caregiver.
(5) Successful ratio of infant’s imitation.
The graph shows successful ratios of imitation when thelearner selects Ms and Mo in the last 20 steps.
In the simulation modeled in the paper, only infants withpreference curve (C) can successfully acquire the correct bodymapping in which the self-model and other-model are clearly
separated, as can be seen in Fig.7 (1). It can be seen thatthe successful ratios of self-imitation and imitation of the
caregiver converge to 1.0 (Fig.7 (5)-(C)), which means thatthe learner acquires the capability of correct imitation. Whenthe agents have preference curves (B), (D), (E), or (F), theobserved motions are correctly associated with the self-motor
commands but the self-motions and other’s motions are notdistinguishable. When the agents have preference curves (A),(G) or (H), the observed self-motions are correctly associatedwith the self-motor commands but some observed other’s
motions are not associated with any motor commands (theweights are not zero but are too small to be considered
exclusive). This means that the learner is unable to constructa model of the other.
The learner becomes able to imitate self-motions after about
300 steps with any preference curve as can be seen in Fig.7(5), even though some wrong connections remain due tothe exclusivity of the connections being insufficient. This isbecause the self-motions are always somewhat correlated withthe corresponding motor commands. However, the success ofthe developmental process depends greatly on the preference
curve.
a) Typical developmental process: The learner using
preference (C) frequently chooses self-related motions forthe first 300 steps but then the frequency quickly decreases

7

as can be seen in the left of Fig.8. Then, the frequencyof the other-related motions increases relative to the selfrelated motions, and the learner acquires the other-model. This
indicates a developmental process in which the infant’s selfimitation appears early on, and disappears once the self-modelis acquired. Then the mutual imitation between the infant
and the caregiver begins. The resultant processes, therefore,
involve the process of transition from self to mutual imitation, that is, the developmental process of the infant’s selfother distinction. It is also explained that in this transition
an attentional shift from perfect contingency (self-motions)to imperfect contingency (other’s imitative motions) occurs
owing to preference (C).
The self-imitation in the results is quickly inhibited. It isinferred that the learner confuses the self-model and the othermodel if he/she continues to self-imitate. It can be also said
that the self-model and the other-model are confused if the
caregiver keeps repeating the same imitative motion. We cansee from the graph on the right of Fig.8 that the caregiverin these results frequently shows random motions. In thelong run, he/she displays all motions. This is due to the low
preference for motions from which the agent can accurately
predict a successive observation (i.e., motions which elicit toofamiliar motions), and this characteristic could be necessary
for a typical development.
In this simulation, the self-model is quickly acquired because a correct pair of the motor command and the observationof self-motion is always presented to the infant’s learning
system. On the other hand, the learning of the other-modeltakes longer because a correct pair of the command and theobservation of other’s motion is not always presented to thelearning system. Moreover, after the infant’s self-imitation is
inhibited, the other-model is slowly learned owing to the caregiver’s occasional imitation (because the caregiver’s preference
to the imitation is low) until the mutual imitation becomesdominant. This also could happen in the infant developmental
process if the learning is an unsupervised manner. However,some rewards are actually expected in the learning of the bodymapping and the learning can be accelerated compared to our
results. The self-model is acquired in about 1,000 steps andthe other-model is acquired in about 8,000 steps, however, thisresult could be an extreme case because no reward is assumed.
b) Atypical developmental process: In the results withpreferences (B), (D), (E), and (F), it was observed that thelearner chooses random motions with low frequency, as canbe seen in Fig.7 (3) and tends to keep same motions. The
caregiver is encouraged to imitate these actions, then thisresults in an infant who has trouble differentiating the observed
actions. This is because the learner has high preference for awide range of the prediction error. Meanwhile, when the infant
has preferences curve (A), (G), or (H), the caregiver does notoften imitate (the rate of selected other-related motion is low in
Fig.7 (4)) and the infant, therefore, cannot acquire the othermodel. These infants could not elicit the imitation behavior
from the caregiver because:• The learner with the preference curve (A) always prefers
random motions.
• The learner with the preference curve (H) prefers onlyIEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

self-imitation due to the quickly acquired self-model.
The learner with the preference curve (G) prefers using
the immature other-model rather than the mature selfmodel.
Since the caregiver is assumed to have preference curve (C),
it is up to the infant to choose behaviors that are within thelimits of acceptable predictability. The infant must be able
to elicit well-balanced imitation behavior from the caregiver.
Otherwise, it is incapable of forming the correct mapping.
It is considered that the confused body mapping and thedeletion of the other-model express mappings of developmentally disordered children; the former indicates a disorder inself-other distinction and the latter indicates a disorder inunderstanding other people. For example, earlier psychoanalytic theories have suggested that a developmental disorderof distinction between self and non-self is fundamental tochildren with autistic spectrum disorders (ASD) (ex., [26]).
Recent studies have found functional brain abnormalities inchildren with ASD in the task of distinguishing their own facefrom those of others (ex., [27]). A confused body mapping
could be related to these failures in self-other distinction.
Furthermore, psychological studies have reported that children
with ASD lack a theory of mind (ex., [28]). A body mapping
without an other-model could be related to the failure in
estimating other people’s internal states. In the result withpreference (A), the other-model is not learned in 10000 steps
but is slowly learned owing to the caregiver’s occasional
imitation. The infant with preference (A) can learn the othermodel by taking much time. It might be related to a kind ofdelayed-development of the infant. Additionally, the transition
from self to mutual imitation is not seen in this result, whichmeans that it is not a typical developmental process.
Concerning the preferences, it has been observed that developmentally disordered children tend to show strong interest in
one object and repeat the same behavior patterns (especiallychildren with ASD [29]), and that this tendency could be
explained from the preferences (B), (D), (E), and (F). It has
also been observed that developmentally disordered children
tend not to initiate communication with other people (especially children with ASD [29]), and this tendency could bealso explained from low preference for the wide range ofthe prediction error in preferences (A), (G), and (H). The
preference curve (H) is for highly-predictable motions but
the agents do not initiate communication because they prefer
only self-imitation. The learner with preference curve (G)prefers using the immature other-model (i.e., always explores
new things) and, therefore, does not communicate with otherpeople.
Using our system, we can test disordered developmental
mechanisms and processes and observe the resultant developmental disorder. For example, the infant with preference curve(H) (Familiarity greedy) tends to frequently imitate self motion
and consequently fails to develop its other-model; which istypical in the developmental process of children with ASD.
This result suggests that a failure in acquisition of a healthy
body mapping for imitation stems from atypical preferencesof individuals, though it is necessary to investigate why theatypical preferences occur in the first place.
•8

C. Summary
From the results shown above, it is considered that thefollowing aspects are necessary for typical development (thetransition from self to mutual imitation).
• The acquisition of the self-model by self-imitation andthe subsequent inhibition of self-imitation.
• The elicitation of imitation from the caregiver throughthe infant’s self-imitation and other-imitation.
• The experience of a wide variety of motions (the perseverance of certain motions can result in atypical development).
Removing one of these requirements results in abnormal
development. These requirements depend on the predictability
preference of the agents. The preference with the inverted-U
shape, which is typical in a healthy person, leads to a typicaldevelopmental process while the atypical preferences leads toa disordered body mapping. We emphasize that a typical developmental process of transition from self to mutual imitation
emerged from our system without any explicit mechanism ofdevelopmental order. The results suggest that the predictability
preference is a very important factor in the development of an
infant’s body mapping, which enables it to distinguish selfmotion from other’s motion and gives it the ability to imitate
both. It is also suggested that an abnormal body mapping
structure stems from atypical predictability preferences.
D. Discussions on the simulation modela) Assumptions of the body mapping and interaction
model: In order to simplify the model, we assumed thatthe body motions of the agents are spatially and temporally
discretized. Here, we consider the capabilities of the motion segmentation in infancy. Concerning the spatial motion
segmentation, Rochat and Morgan [30] have revealed that
3–5 months old infants are sensitive to differences in the
directionality of the self-produced movements of their legs.
This suggests that the target infants in the simulation (1–8months old infants) could segment the body motions at least
with respect to the directional information of the motions.
The capability of the temporal segmentation is discussed ina rhythm of body movement. A rhythmic body movement is
considered to be a sign of the motion segmentation. McAuleyet al. [31] studied the tempo of people’s spontaneous rhythmic
movements. They revealed that 4–5 year old children frequently showed rhythmic movements of about 300ms tempo(period) and the rhythm was shifted to a slower tempo withincreasing age. Young infants (less than 12 months) also
show rhythmic motions (e.g., arm banging and rattle shaking).
Merker et al. [32] have shown that 6 months old infants
can rhythmically show movements of 1–3 Hz to music. It
is guessed, from these facts, that the target infants could
have the capability to discretize body motions with the above
temporal resolution. However, it is considered that the motion
segmentation and the imitation capability are developed inparallel in the infant’s developmental process.
In our model, the delay introduced by copying the motor
commands plays an important role in the acquisition of theother-model and self-other distinction. The model assumed

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

that the delay is discretized and fixed to a single step because
both agents are assumed to synchronously perform their body
motions at fixed time intervals. This assumption of interaction
is not realistic. In real-world situations, the motions of both
agents are not simultaneous and the delay varies in several
time-scales owing to the context of interaction. Hiraki [33]has investigated infants’ sensitivity to a temporal aspect ofcontingency using a delayed self-image and revealed that 5
and 7 months old infants cannot distinguish between a 1 sec
delayed image of the self-movement and a live image of theself-movement (they can distinguish when the delay is 2 sec).
This suggests that some time delay is allowed to discriminate
self from other (small time delay can be treated as there
is no delay). If our model has a mechanism to distinguishbetween a small delay (less than about 1 sec) and a large
delay (more than about 1 sec), the model can deal with an
unsynchronized interaction (the agents do not need to movesimultaneously). This mechanism can be realized by assumingthat the activation of the copied motor command is preserved
for a short term (for example, the immediate copied motor
command is activated for about 1 sec). On the other hand,a large time-scale of delay is related to the development of
delayed imitation (deferred imitation). In order to deal withthe delayed imitation, temporal matching of motion also needs
to be considered. The resultant process in our simulation does
not sufficiently account for infants’ developmental process ofbody mapping in that the process of the spatial and temporalsegmentation of the body motion is not implemented. A
model that includes a mechanism for motion segmentation andallows continuous and several time-scales of delay needs to beinvestigated in the future.
The simulation in the paper has dealt with a kind of gestureimitation; however, it is known that a goal-oriented imitation
with object manipulation (e.g., imitating position change ofan object but not the hand and arm’s movements to move theobject) is acquired before gestural imitation [34] in the infantdevelopmental process. This suggests that the main attention in
imitation shifts from the goal of the motion to the motion itself.
Some studies have shown that gestural imitation is also goaloriented [35]. In gesture imitation, we also need to consider
how to reproduce the movement (i.e., in a mirroring manner
or not-mirroring manner) although our simulation did not deal
with this issue. This is also an attention problem. In orderto obtain a deeper understanding of imitation development,
we need to further investigate the mechanism of shifting theattention in imitation.
b) Biological mechanism related to the body mapping
model: The model of the body mapping in the paper wasderived with much consideration of computational requirements (e.g., the mechanism of the delayed copy of the motor
command and the duplicated motor representation layer) andwas not based on anatomical evidences of biological systems.
Here, we describe how the body mapping model is associatedwith biological mechanisms of the human brain.
In the brain of macaque monkey, a mirror neuron thatfires both when the animal acts and when it observes thesame action [36]. This neuron contributes to a direct matching
between action and perception. Many studies have revealed

9

that human brain also has a mirror neuron sysytem (MNS) to
directly associate an action with the corresponding observation[37,38]. Brady et al. [39] have shown that there is dissociationin face recognition processing such that the left brain isdominant for the recognition of self and the right brain isdominant for the recognition of others. Saxe et al. [40] havesuggested that extrastriate body area (EBA) in the humanbrain, which selectively responds to visual images of humanbodies or body parts [41], distinguishes between body parts
presented from egocentric and allocentric perspectives. The
authors also have found that the right EBA selectively responds
to visual images of body parts presented from an allocentric
perspective. The future works will study how the laterality of
MNS in the recognition of self and others is related to the
proposed model of body mapping.
The mechanism of motor command copy in the model isequivalent to an efference copy of a motor command in thehuman body system. No studies have found a brain mechanism
which is equivalent to the delayed copy mechanism in ourmodel, however, we think that the delayed copy can be
represented by a memory mechanism, that is, the activationof the copied motor command is preserved for a short period.
It is considered that these biological evidences are related
to our model; however, we need further investigation to match
our model with the human system.
IV. F URTHER I NVESTIGATION
In addition to the basic mechanism of healthy social development, we would also like to investigate the best possible
interaction methods for caregivers when dealing with atypicalinfants. Some computer simulation studies have investigatedwhat kind of caregiver behavior can alter an infant’s development or improve their capabilities (ex., [14, 42]). A greater
understanding in this area would be of enormous benefit toguide care in real situations.
If a caregiver were to assume an atypical imitation pattern,
how would this affect the results of interaction? Fig.9 shows
the results of varying both the infant’s and the caregiver’s
preference curves. The table shows which type of result is
acquired by the infant. The three possible types are:(I) Self and Other: Has successfully acquired both selfmodel and other-model. Generally results from healthy
behavior from both infant and caregiver.
(II) Self Only: Has successfully acquired the self-model, but
the other-model is weak or absent. The infant has not
successfully elicited enough imitation from the caregiver; for example, by being too unpredictable.
(III) Confusion: The infant is totally confused, unable todistinguish self from other. This usually results frombeing too repetitive and predictable.
The first column shows that the agent successfully acquires
a good body mapping in which the self-model is discriminatedfrom the other-model most of the time. This is strange andcounter-intuitive since the infant with preference curve (A)(Nothing) is almost always displaying a random behavior andrarely trying to imitate. In these developmental processes,
the caregiver frequently imitates the infant motion which isIEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXXInfantCaregiver

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Fig. 9.

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Results from all possible combinations of preference curves.

randomly chosen, in other words, the caregiver voluntarily
shows various imitative motions to the infant. However, thedevelopmental process of transition from self to mutual imitation does not emerge. These results suggest that the infant
can acquire a healthy body mapping if the caregiver frequently
imitates various motions of the infant on his/her own initiative,
even though the infant does not try to imitate self/caregiver’s
motion. We suggest that this is an unrealistic developmental
process because a caregiver would not consistently continue
to imitate the non-interactive body babbling over an extended
period of time.
As another remarkable result, it appears that even when
the infant has atypical preference curve (G) (novelty greedy),
it can actually develop a healthy body mapping through theinteraction with a caregiver that has an atypical behavior.
Curiously enough, it fails when the caregiver displays behavior
based on typical preference curve (C), but manages to do wellmost other times. The result suggests that the preference ofnovelty greedy usually does not properly elicit the imitationfrom the caregiver with typical preference, but it does from the
caregiver with atypical preferences. The healthy body mappingis acquired in these cases but the developmental process oftransition from self to mutual imitation does not emerge.
It is also interesting to note that row (C) (see Fig.9) shows
all three types of result, more so than any other row. Thissuggests that this preference curve leads to a much wider
repertoire of behavioral types and richer dynamics, rather thansimple saturating or repetitive results. The infant must be
careful to be neither too predictable nor too unpredictable,
but instead aim for the caregiver’s comfort zone. This way,
he/she can successfully elicit just the right about of imitation,with which the correct mappings can be learned. The typicaldevelopmental process of transition from self to mutual imita-tion emerges only for the pair of infant and caregiver both whohave typical preference curve. These results, characterized by
the difference between typical and atypical preferences, lend
credence to our simulation.
In this section, we have investigated the multiple combinations of preference curves, however, our model is too simple
to simulate various interaction patterns. Further investigationis needed to improve the simulation model (by removing thelarger assumptions).
V. C ONCLUSION
In order to study the mechanisms of imitation development
involving the acquisition of self-other distinction and imitation
capabilities, a model was made that was able to develop ahealthy body mapping, which is a prerequisite for imitation,
during the interaction between infant and caregiver in an
imitation game, while discriminating self-motion from theother’s motion. Although the model is not based on anatomical
evidence of biological systems, we assume that humans havesomething equivalent to our system, with mechanisms toutilize the difference in observational delay and to choose
self-imitation and other-imitation in order to solve problemsof self-other distinction and body mapping acquisition frommutual imitation.
It has been shown that the order of body mapping acquisition (first the self-model followed by the other-model) can
emerge from our system without any explicit mechanism ofdevelopmental sequence or specific tasks. We also have shown
the inverted-U preference curve is indeed a viable proposal
for healthy development. However, the proposed model does
not sufficiently account for infants’ developmental process ofbody mapping in that the process of the spatial and temporalsegmentation of the body motion is not considered.

IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT, VOL. X, NO. X, MONTH XXXX

The analysis of the simulation results is still speculative but
suggest that the predictability preference is one of the factors
which govern the development of an infant’s body mapping,enabling it to distinguish and imitate self-motions and the
motions of others. Future work will need to justify the modeland the resultant developmental process by comparing themwith human infants’ natural developmental processes. It would
be interesting to see if the model allows a particular caregiver’s
support policy to transform an abnormal development to atypical one, and then to compare that to real data regarding infant development. Furthermore, if an atypical preference leads
to developmental disorder, a mechanism to produce atypicalpreferences should be investigated. Our assumption that thecapability of motion segmentation is already acquired needs to
be investigated and if possible, a mechanism for its acquisition
should be added to the system. Finally, it is also importantto realize the developmental process with real robots to findissues that were not modeled in our computer simulation. The
motion segmentation issues need to be investigated also forthe real world implementation.
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A BOUT THE AUTHORS

Takashi Minato was a researcher of CREST, JSTsince December 2001 and obtained his PhD degree
in Engineering from Osaka University in 2004. He
was an assistant professor of the Department of
Adaptive Machine Systems, Osaka University since
September 2002. He worked as a researcher for
ERATO, JST since June 2006. He has currently beenworking as a researcher in ATR Hiroshi Ishiguro
Laboratory since January 2011.

Dale Thomas recieved a BSc in Cybernetics andControl Engineering from Reading University, UK,
in 2000. From then until 2003 he worked as a
researcher in Zürich, Switzerland, and in 2004 herecieved an MSc in Evolutionary and Adaptive Systems from Sussex University, UK. After that hespent several years as a programmer in the computer
games industry in Japan, before moving to Osaka
University, in 2008, to work as a researcher for the
Asada Project, ERATO, Japan Science and Technology Agency. His main research interests include:
computer graphics, artificial intelligence and artificial life, with particularemphasis on embodiment, physical simulation and morphogenesis.

Yuichiro Yoshikawa received the Ph.D. degree inEngineering from Osaka University, Japan in 2005.
From April 2003 to March 2005, he was a Research
Fellow of the Japan Society for the Promotion of
Science. Since April 2005, he was a researcher
of ATR Intelligent Robotics and Communication
Laboratories. He worked as a researcher for ERATO,
JST since April 2006. He has been an associate
professor of the Department of Systems Innovation,
Osaka University since August 2010.

Hiroshi Ishiguro received the D.Eng. degree from
Osaka University, Osaka, Japan, in 1991. After that
he began working as a research assistant in the
Department of Electrical Engineering and Computer
Science, Yamanashi University, Yamanashi, Japan.
Then, in 1992, he moved to the Department of
Systems Engineering, Osaka University, as a research assistant. In 1994, he was made an associate
professor in the Department of Information Science,
Kyoto University, Kyoto, Japan, and started researchon distributed vision using omnidirectional cameras.
From 1998 to 1999, he worked in the Department of Electrical and Computer
Engineering, University of California, San Diego, as a visiting scholar and in
2000, he moved to the Department of Computer and Communication Sciences,
University, Wakayama, Japan, as an associate professor, before becoming
professor in 2001. He moved to the Department of Adaptive Machine Systems,
Osaka University in 2002. He is now a professor of the Department of
Systems Innovation, Osaka University, and a leader at ATR Hiroshi Ishiguro
Laboratory, Kyoto.

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